Digital Signal Processing Reference
In-Depth Information
g
m
∝
I
bias
C
gs
∝
W
∝
I
bias
f
T
≈
constant
,
for fixed
V
gs
−
V
T
(A.12)
The results presented here should not be surprising after all, since scaling a
transistor's width
W
without changing the length
L
basically boils down to
placing several independent transistors in parallel. Intuitively one can see that
connecting those transistors in parallel should have no effect on gain or on fre-
quency performance. To conclude this introduction, Table A.1 summarizes the
considerations one should make during the design of an analog most ampli-
fier. Although the deductions were made using the simplified model of a mos
transistor in the strong inversion saturation region, the general idea remains
valid for characteristics anywhere between a quadratic and a linear current-
voltage transistor model.
Dc-gain (
g
m
r
ds
)
Cut-off frequency (
f
T
)
1
V
gs
−
Fixed
I
bias
, variable
V
gst
∝
∝
V
gs
−
V
T
V
T
Fixed
V
gst
, variable
I
bias
Constant
Constant
Table A.1.
Correlation between biasing and small-signal performance of a mos
transistor in the strong inversion saturation region.
Remark that for a fixed overdrive voltage
V
gs
−
V
T
, both the dc and the high
frequency performance of the mos transistor are independent of the power
consumption. Only technological parameters such as oxide thickness (
t
ox
), di-
electric constant (
ox
) and minimal gate length (
L
min
) define the performance
limits of a certain cmos process.
A.1
Feedback amplifiers
Despite the good low frequency gain performance, the multistage current am-
plifier introduced in Figure A.1 is not suited for high frequency applications.
This is because the location of the 3 dB cut-off frequency of a single stage is
defined by
r
ds
and
C
gs
. The overall transfer function of a
n
identical cascaded
gain stages is given by (A.13):
n
g
m
r
ds
A(jω)
=
(A.13)
1
+
jωr
ds
C
gs
It follows that, for a system with
n
(
>
1) multiple coincident poles, the 3 dB
bandwidth (
ω
3dB
) does not correspond with the frequency pole of a single
